Louisa seemed to express by her looks the irksomeness of such demonstrations; and which did not pass unobserved. “This may appear tedious and uninteresting,” said Mr. Seymour, “but the information is absolutely essential to our future progress: if you would reap, you must sow.” Tom and Louisa both expressed themselves willing to receive whatever instruction their father might consider necessary; and they farther declared, that they understood the demonstration he had just offered them. “Is it not then evident,” proceeded Mr. Seymour, “that the composition of forces must always be attended with loss of power; since the diagonal of a parallelogram can never, under any circumstances, be equal to two of its sides? and is it not also evident, that the length of the diagonal must diminish as the angles of the sides increase: so that the more acute the angle at which the forces act, the less must be the loss by composition? But I shall be better able to explain this law by a diagram. If B A, A C be the sides of a parallelogram, representing the direction of two forces, and A D the diagonal path of the body, is it not evident that the line A D will shorten as the angle B A C increases?” [Illustration: Fig. 5. Three parallelograms, beginning with a square and ending with a narrow diamond, all sharing one side.] “We see that at once,” cried Tom, “from the diagram before us.” [Illustration: Fig. 6. A square and a rectangle with a common diagonal.] “Then we will proceed to another fact connected with the same subject. Look at this diagram; is not the diagonal A D common to both the parallelograms inscribed about it, viz. of A B C D, and A E F D?” “To be sure it is.” “Then it is equally clear, that a body may be made to traverse the same path A D, by any pair of forces represented by the adjacent sides of either of such parallelograms.” “Undoubtedly.” “I request you to keep that fact in your recollection.” “I have now to inform you,” continued he, “that a single force may be resolved into any number of forces, and may, in fact, be regarded as compounded of innumerable oblique ones. In order, however, to render this fact more intelligible, I must refer you to fig. 6, from which it will appear that the motion of a body, along the line A D, will be the same whether it arise from one single force acting in that direction, or from two forces impressed upon it in the directions A B, A C, or in those of A E, A F; and, consequently, although the motion may, in reality, be the effect of a single force, yet it may be considered as compounded of two or more in other directions, since the very same motion would arise from such a composition.”